Stir together panko, scallions, mint, garlic, egg, ⅓ cup yogurt, ¼ cup dill, 1 teaspoon salt, and ¼ teaspoon pepper in a medium bowl until thoroughly combined. Let stand 10 minutes.

Add beef to panko mixture and stir together until just combined. Shape beef mixture into 20 (about 1 ¾-inch) meatballs (about 2 tablespoons each). Arrange meatballs evenly spaced apart on a large rimmed baking sheet lined with aluminum foil. Chill for 20 minutes.

Grate 2 cucumbers on the largest holes of a box grater into a clean kitchen towel. Squeeze cucumbers over a sink to remove excess water; place cucumbers in a small bowl. Add lemon zest and juice, 2 tablespoons oil, ½ teaspoon salt, and remaining 1 cup yogurt, 1 tablespoon dill, and ¼ teaspoon pepper; stir to combine, adding 2 to 3 teaspoons water, if needed, to thin to desired consistency. Refrigerate yogurt sauce until ready to use. Cut remaining 2 cucumbers into half-moons; set aside.

Preheat oven to broil with rack 6 inches from heat source. Halve onion and finely chop 1 half. Thinly slice remaining onion half; set aside. Heat remaining 2 tablespoons oil in a small saucepan over medium. Add finely chopped onion half and remaining ¾ teaspoon salt; cook, stirring often, until softened, about 2 minutes. Add orzo; cook, stirring constantly, until orzo is toasted, about 2 minutes. Stir in chicken stock, and bring to a simmer over medium-high. Reduce heat to low; cook, uncovered, stirring occasionally, until orzo is al dente, 9 to 10 minutes.

While orzo cooks, broil meatballs until browned on both sides, 16 to 18 minutes, flipping halfway through cooking time.

Divide orzo evenly among 4 bowls; top evenly with meatballs, reserved cucumber slices, desired amount of sliced onion half, and yogurt sauce. Squeeze 1 small lemon wedge over each serving. Top with romaine lettuce, feta, olives, and tomatoes.